WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 24, 2025
A Novel Interpolation-Based Order Six Method and its Convergence
Analysis
Authors: , ,
Abstract: This paper introduces an interpolationbased
order six method for solving nonlinear
equations. Our
method offers significant improvements in accuracy, stability, and efficiency, making it valuable for computational
and applied mathematics. The main goal is to address various nonlinear
problems in fields such as physics,
engineering, and finance. The paper explains the theoretical foundation and key principles of the method, which
uses interpolation points instead of derivatives to approximate solutions. This approach enhances convergence
behavior and numerical precision. We also conduct a detailed local and semilocal convergence analysis to evaluate
the method’s performance. This analysis provides insights into the convergence region, radii, and error boundaries.
It also assesses the method’s effectiveness in scenarios where accurate initial guesses are hard to obtain. Extensive
numerical experiments on diverse test problems demonstrate the method’s superior convergence rates and error
estimates, confirming its effectiveness and reliability.
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Keywords: Nonlinear
equations, Fréchet derivative, Interpolationbased
method, Banach Space, Convergence
analysis, Convergence radii, Lipschitz continuity, Ball convergence
Pages: 240-257
DOI: 10.37394/23206.2025.24.24